Jim Renwick, a meteorologist with the National Institute for Water and Atmosphere, responded.

The heat the Sun provides is fuel, just like petrol in a car.
Heat from the Sun makes weather systems go, just as petrol makes
a car go. Without the Sun, there would be no weather! The most
important thing about the Sun's heat is that it is not spread
around evenly. Tropical places, like Samoa and Singapore, are
warmest because they get lots of heat from the Sun. Places near
the Poles, like Antarctica and Alaska, are coldest because they
don't get much heat from the Sun at all.

The big difference in temperature makes for a big difference in
air pressure (the lines on the weather map) and that makes the
winds blow. The winds, and all the weather that goes with them,
are trying to make the hot places cooler and the cold places
warmer, trying to make the temperature the same everywhere. New
Zealand is a windy place because it's about halfway between the
warmest and the coldest places on the Earth.

The weather and the winds are trying to even out temperatures
everywhere. But, that will never happen because the Sun keeps on
heating up the tropical places more than the polar places. So,
the winds and the weather will have to keep going as long as the
Sun keeps shining. If the Sun did stop, the winds would slow
down and stop in about two or three weeks or so. Then, there
would be no weather, and it would be very cold!